If the vertices of a hyperbola be at - 2 , 0 and 2 , 0 and one of its foci be at - 3 , 0 , then which one of the following points does not lie on this hyperbola ?

Step-by-step solution

Since, the vertex of the hyperbola are A ′ - 2 ,   0 and A 2 ,   0 . Hence, the transverse axis of the hyperbola is x - axis and centre is O 0 , 0 . Equation of hyperbola can be taken as x 2 a 2 - y 2 b 2 = 1 ⇒ a = 2 and a e = 3 ⇒ e = 3 2 Since, b 2 = a 2 e 2 - 1 ⇒ b 2 = a 2 e 2 - a 2 = 9 - 4 = 5 Hence, equation of hyperbola is x 2 4 - y 2 5 = 1 Clearly, point 6 ,   5 2 doesn't lies on the hyperbola.